0. Functions

Given the figure showing four curves labeled A, B, C, and D, which represent the functions $f\left(x\right)=\sin x$, $f^{\prime }\left(x\right)$, $f^{″}\left(x\right)$, and $f^{‴}\left(x\right)$, respectively, which curve corresponds to $f^{″}\left(x\right)$?

Below is a graph of the function $y=\(\tan\]\left\)(bx\(\right\))$. Determine the value of b.

Sketch the function $y=\(\cos\]\left\)(x\(\right\))-1$ on the graph below.

Determine the value of $y=\(\sin\[\left\)(-\(\frac{\pi}{2}\]\right\))+50$ without using a calculator or the unit circle.

Below is a graph of the function $y=\(\sec\[\left\)(bx-\(\pi\]\right\))$. Determine the value of b.

Below is a graph of the function $y=\(\csc\]\left\)(bx\(\right\))$. Determine the value of b.

Below is a graph of the function $y=\(\cot\[\left\)(bx+\(\frac{\pi}{2}\]\right\))$. Determine the value of b.

Identify the amplitude and period of the following functions.

$f\(\left\)(\(\pi\]\right\))=2\(\sin\)2\(\theta\)$

Identify the amplitude and period of the following functions.

$g\(\left\)(\(\theta\]\right\))=3\(\cos\[\left\)(\(\frac{\theta}{3}\]\right\))$

Identify the amplitude and period of the following functions.

$p\(\left\)(t\(\right\))=2.5\(\sin\]\left\)(\(\frac\)12\(\left\)(t-3\(\right\))\(\right\))$

Identify the amplitude and period of the following functions.

$q\(\left\)(x\(\right\))=3.6\(\cos\[\left\)(\(\frac{\pi x}{24}\]\right\))$

Identify the amplitude and period of the following functions.

p(t) = 2.5 sin ((1/2)(t-3))

Beginning with the graphs of $y=\(\sin\) x$ or $y=\(\cos\) x$, use shifting and scaling transformations to sketch the graph of the following functions. Use a graphing utility to check your work.

$q\(\left\)(x\(\right\))=3.6\(\cos\[\left\)(\(\frac{\pi x}{24}\]\right\))+2$

Design a sine function with the given properties.

It has a period of $12$ with a minimum value of $-4$ at $t=0$ and a maximum value of $4$ at $t=6$.

Find a trigonometric function $f$ represented by the graph in the figure. <IMAGE>